In the present work, as we mentioned before, we consider universality for all interactions of leptons. Therefore, we only consider the magnetic moment of the muon and ignore weaker constraints on the AMMs of tau and electron.
The model contribution to muon magnetic moment arises from the one-loop mediated by VDMs. The analytical expression for \(\Delta a_{\mu }^{\psi }\)  is [1]}-[2]}:
\(\Delta a_{\mu }^{\psi }=\frac{1}{8\pi ^2} \frac{m_{\mu }^2}{M_{X}^2}\int \frac{g_s^2P_s(x)+g_p^2P_p(x)}{(1-x)(1-\lambda ^2 x)+\epsilon ^2\lambda ^2x}dx\) 
